Medical imaging analysis has advanced significantly due to developments in computer vision. However, deep learning models are typically trained on consistent data distributions, which hampers generalizability when evaluated on datasets with varying distributions. This issue is especially prominent in medical imaging, where heterogeneity arises from differences in acquisition sites, imaging protocols, scanner types, and patient demographics. Additionally, strong performance of neural networks is linked to the availability of large, labeled datasets. However, annotated data is scarce in medical imaging, and domain expertise is not readily available, further hindering robust model development. This research addresses these challenges by proposing novel domain adaptation methods to improve neural network generalization across diverse medical imaging domains. The methods achieve effective adaptation while minimizing the dependency on large labeled datasets, addressing the limited data availability in real-world medical settings. This work has developed three alternatives to supervised domain adaptation, with several key innovations: (1) A novel, unsupervised, parameter-efficient domain adaptation framework for multi-target medical imaging domains is proposed. It overcomes the limitations of supervised training and the scarcity of labeled data. (2) A novel test-time adaptation framework to adapt natural foundation models, enabling zero-shot transferability to medical tasks without relying on labeled data. It addresses several key challenges: the need for supervised training, domain-specific fine-tuning, the unavailability of annotated data, lack of domain expertise, and computational constraints. (3) A few-shot learning framework is proposed to adapt foundation models for fine-grained medical tasks, highlighting the intrinsic limitations of foundation models when applied to complex medical tasks. These frameworks have improved our understanding of how domain adaptation can be effectively utilized for medical imaging analysis with limited labeled data and high data variability. This thesis serves as a valuable resource for medical practitioners and tool developers in designing innovative algorithms and applications for healthcare.